Admiral Muskwe scored a pivotal first-half penalty to put Fleetwood on course for an easy 3-0 League One win at 10-man Shrewsbury.
Muskwe converted the controversial 25th-minute spot-kick, awarded for Matthew Pennington handling a Brendan Sarpong-Wiredu shot.
Referee Ross Joyce also dismissed defender Pennington in the same incident for Town's third red card in as many games.
The 10 men fell further behind three minutes later as Promise Omochere fired home his first goal for Scott Brown's visitors.
Omochere had previously gone 17 games in all competitions without finding the net since his summer move from Bohemians.
Only an upright denied Danny Andrew Fleetwood's third goal after 70 minutes. But the visitors imposed their superiority when ex-Shrewsbury midfielder Josh Vela's last-minute shot was deflected into his own net by Chey Dunkley.
Shrewsbury, who also lost Pennington's defensive partner Tom Flanagan to an early injury, drop to 15th after a third successive defeat.